E2 VoC Analyses Part 2: Regression Analyses

Participant info

Agency task: Agency decisions

Model: Agency decisions by VoC

## Mixed Model Anova Table (Type 3 tests, LRT-method)
## 
## Model: stage_1_choice ~ age_z * voc_z * condition_trial + (voc_z * condition_trial || 
## Model:     subject_id)
## Data: agency_model_data
## Df full model: 12
##                        Effect df      Chisq p.value
## 1                       age_z  1       0.00    .965
## 2                       voc_z  1 166.62 ***   <.001
## 3             condition_trial  1       0.07    .796
## 4                 age_z:voc_z  1  12.28 ***   <.001
## 5       age_z:condition_trial  1       0.01    .941
## 6       voc_z:condition_trial  1  51.94 ***   <.001
## 7 age_z:voc_z:condition_trial  1     5.26 *    .022
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: stage_1_choice ~ age_z * voc_z * condition_trial + (1 + re1.voc_z +  
##     re1.condition_trial + re1.voc_z_by_condition_trial || subject_id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+06))
## 
##      AIC      BIC   logLik deviance df.resid 
##  38797.4  38902.4 -19386.7  38773.4    46747 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -37.884  -0.383   0.172   0.500  37.176 
## 
## Random effects:
##  Groups       Name                         Variance Std.Dev.
##  subject_id   (Intercept)                  4.51649  2.1252  
##  subject_id.1 re1.voc_z                    0.49714  0.7051  
##  subject_id.2 re1.condition_trial          0.82459  0.9081  
##  subject_id.3 re1.voc_z_by_condition_trial 0.04873  0.2207  
## Number of obs: 46759, groups:  subject_id, 150
## 
## Fixed effects:
##                              Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  1.262274   0.175189   7.205 5.80e-13 ***
## age_z                        0.007817   0.175021   0.045 0.964374    
## voc_z                        1.094665   0.061063  17.927  < 2e-16 ***
## condition_trial             -0.020084   0.076998  -0.261 0.794221    
## age_z:voc_z                  0.218514   0.061010   3.582 0.000341 ***
## age_z:condition_trial       -0.005671   0.076827  -0.074 0.941160    
## voc_z:condition_trial        0.200551   0.025090   7.993 1.31e-15 ***
## age_z:voc_z:condition_trial  0.058322   0.025114   2.322 0.020219 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) age_z  voc_z  cndtn_ ag_z:v_ ag_z:c_ vc_z:_
## age_z       -0.001                                            
## voc_z        0.012  0.001                                     
## conditn_trl  0.011 -0.002  0.007                              
## age_z:voc_z  0.002  0.010 -0.006  0.001                       
## ag_z:cndtn_ -0.002  0.007  0.001 -0.009  0.004                
## vc_z:cndtn_  0.006  0.001  0.043  0.034 -0.001   0.005        
## ag_z:vc_z:_  0.001  0.003  0.000  0.005  0.036   0.033   0.000

Plot: Sensitivity to the value of choice

Plot: Sensitivity to value of choice with continuous age

Summary stats: Sensitivity to value of control

Agency task: Machine selection

Model: Optimal machine choices across trials by condition and age

## Mixed Model Anova Table (Type 3 tests, LRT-method)
## 
## Model: stage_2_acc ~ age_z * context * condition_trial + (context * 
## Model:     condition_trial || subject_id)
## Data: machine_model_data
## Df full model: 12
##                          Effect df     Chisq p.value
## 1                         age_z  1 15.49 ***   <.001
## 2                       context  1 29.27 ***   <.001
## 3               condition_trial  1 69.50 ***   <.001
## 4                 age_z:context  1      0.74    .389
## 5         age_z:condition_trial  1      0.70    .404
## 6       context:condition_trial  1    5.47 *    .019
## 7 age_z:context:condition_trial  1      1.71    .191
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: stage_2_acc ~ age_z * context * condition_trial + (1 + re1.context1 +  
##     re1.condition_trial + re1.context1_by_condition_trial ||      subject_id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+06))
## 
##      AIC      BIC   logLik deviance df.resid 
##  15084.2  15179.9  -7530.1  15060.2    21318 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -10.7613   0.0972   0.2017   0.4001   2.4112 
## 
## Random effects:
##  Groups       Name                            Variance Std.Dev.
##  subject_id   (Intercept)                     1.7634   1.3279  
##  subject_id.1 re1.context1                    0.6000   0.7746  
##  subject_id.2 re1.condition_trial             0.2931   0.5414  
##  subject_id.3 re1.context1_by_condition_trial 0.1118   0.3344  
## Number of obs: 21330, groups:  subject_id, 149
## 
## Fixed effects:
##                                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                     2.31548    0.11532  20.079  < 2e-16 ***
## age_z                           0.45937    0.11421   4.022 5.77e-05 ***
## context1                        0.40971    0.07119   5.755 8.65e-09 ***
## condition_trial                 0.49629    0.05390   9.208  < 2e-16 ***
## age_z:context1                 -0.06268    0.07112  -0.881   0.3782    
## age_z:condition_trial           0.04491    0.05342   0.841   0.4006    
## context1:condition_trial        0.09387    0.03923   2.393   0.0167 *  
## age_z:context1:condition_trial -0.05214    0.03913  -1.333   0.1827    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) age_z  cntxt1 cndtn_ ag_z:1 ag_z:_ cnt1:_
## age_z        0.038                                          
## context1     0.033  0.004                                   
## conditn_trl  0.077  0.011  0.031                            
## ag_z:cntxt1  0.000  0.023  0.054 -0.003                     
## ag_z:cndtn_  0.007  0.061 -0.002  0.071  0.021              
## cntxt1:cnd_  0.028  0.000  0.108  0.077  0.014  0.003       
## ag_z:cnt1:_ -0.003  0.017  0.014  0.004  0.106  0.066  0.106

Plot: Proportion optimal machine selections across age groups and trials

Explicit reward knowledge task

Explicit reward knowledge task: summary stats

Model: Explicit reward knowledge by age and true probabilities

## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: error ~ zTrueProb * zAge + (1 | subject_id)
## Data: explicitKnow.filtered
##           Effect        df         F p.value
## 1      zTrueProb 1, 748.00 23.42 ***   <.001
## 2           zAge 1, 148.00   7.59 **    .007
## 3 zTrueProb:zAge 1, 748.00      0.52    .473
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: error ~ zTrueProb * zAge + (1 | subject_id)
##    Data: data
## 
## REML criterion at convergence: 3093.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5243 -0.7034 -0.1905  0.4417  4.1618 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_id (Intercept) 0.1159   0.3405  
##  Residual               1.6947   1.3018  
## Number of obs: 900, groups:  subject_id, 150
## 
## Fixed effects:
##                 Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)      1.58778    0.05154 148.00000  30.810  < 2e-16 ***
## zTrueProb       -0.21012    0.04342 747.99999  -4.840 1.58e-06 ***
## zAge            -0.14204    0.05156 148.00000  -2.755  0.00661 ** 
## zTrueProb:zAge  -0.03119    0.04344 747.99999  -0.718  0.47293    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) zTrPrb zAge 
## zTrueProb   0.000              
## zAge        0.000  0.000       
## zTruPrb:zAg 0.000  0.000  0.000

Plot: Explicit reward knowledge